Understanding a step in a Biot-Savart law problem

[Anti Hydrogen]

Homework Statement

Biot-Savart law

Relevant Equations

Biot-Savart law

I can't understand intuitively why the authors of the book expressed the cross product between the vectors dl and r (unit vector) as: dl sin(pi/2 - theta); isn't it supposed to be expressed as: dl sin(theta)?? So why did the authors put that pi/2 into the argument of sin function, that's my question, please check the file I attached

 

[haruspex]

Homework Statement:: Biot-Savart law
Relevant Equations:: Biot-Savart law

I can't understand intuitively why the authors of the book expressed the cross product between the vectors dl and r (unit vector) as: dl sin(pi/2 - theta); isn't it supposed to be expressed as: dl sin(theta)?? So why did the authors put that pi/2 into the argument of sin function, that's my question, please check the file I attached

In the cross product formula it is sin(angle between the vectors). In the diagram, the angle between the vectors is (π/2-θ).

 

[Anti Hydrogen]

In the cross product formula it is sin(angle between the vectors). In the diagram, the angle between the vectors is (π/2-θ).

That makes sense!; I can't believe I didn't consider that! Thanks!